Geometry of ℓp-direct sums of normed linear spaces
Keywords:
Smooth points, Support functionals, Approximate smoothness, Birkhoff-James orthogonality, Left-symmetric points, Right-symmetric point, Semi inner productAbstract
We consider ℓp-direct sums (1 ≤ p<∞) and c0-direct sums of countably many normed spaces and find the dual of these spaces. We characterize the support functionals of arbitrary elements in these spaces to characterize smoothness and approximate smoothness, both locally and globally. These results let us answer the Chmieliński, Khurana, and Sain question raised in [4] on the existence of a non-approximately smooth normed space whose every element is smooth. We also characterize Birkhoff-James orthogonality and its pointwise symmetry in these spaces.
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